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I know AdjClose contains any corporate change for stock price. I am doing some mathematical analysis for stocks and I want to know what is the difference for Split-Adjusted stock price vs AdjClose and which one should I use?

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It would depend how the data provider is calculating AdjClose, but taken literally, "Split Adjusted Stock price" is adjusted just for splits. AdjClose would presumably be adjusted for splits, but could also be adjusted for any number of corporate actions (e.g. dividends).

In Bloomberg, one can choose with some granularity what to adjust prices by, but you'd need to check with whoever is defining/calculating "AdjClose" for you - it's not a standard term.

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